周期多孔区域压电特征值问题的多尺度渐近算法  

Multiscale asymptotic method for the piezoelectric eigenvalue problem in periodically perforated domain

作　　者：陈庭艳 马强 CHEN Ting-Yan;MA Qiang(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2024年第4期80-88,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11801387,11971336,11971337);四川省自然科学基金(2022NSFSC0322);中央高校基本科研业务费专项资金(YJ201811)。

摘　　要：针对周期多孔区域压电特征值问题,本文基于二阶双尺度(Second-Order TwoScale,SOTS)分析方法提出了多尺度渐近有限元法.该方法将压电问题的特征函数和特征值展开为周期参数的二阶级数,得到其均匀化特征值方程和均匀化系数,然后根据“校正方程”的思想计算了特征值的一阶和二阶校正.本文对该方法进行了算法实现,并在二维多孔结构上进行了验证.结果表明,该方法能够有效识别多孔区域的压电特征值,而且通过将校正项添加到均匀化解中还可以再现位移和电势的原始特征函数.A novel multi-scale asymptotic finite element method based on the Second-Order Two-Scale(SOTS)analysis is proposed for the piezoelectric eigenvalue problem in periodically perforated domain.In this method,the eigen-functions and eigenvalues are expressed in power series of periodicity to the second-order terms and then the homogenized modal equations and effective material coefficients are derived.By the ideal of“corrector equation”,the first-and second-order correctors are calculated.A program is established and numerical experiments are carried out on the two-dimensional perforated structures.It is shown that the proposed method is effective to identify the piezoelectric eigenvalues of porous structures as well as the original eigen-functions for both the displacement and the electric potential can be reproduced by adding the correctors to the homogenized solutions.

关 键 词：压电特征值问题 多孔材料 多尺度渐近展开方法 二阶渐近估计 

分 类 号：O241.82[理学—计算数学]